I've told this story before, but it fits here.
I got a call from another department in the hospital asking for work load figures for a particular time period for my section. Since I kept those on an Excel spreadsheet and updated them monthly I e-mailed the department a copy.
Then I got a call back and was told, "This needs to be typed up on letterhead."
I said, "Go ahead."
"We have a short suspense!" Meaning they needed to do it fast.
I said, "Then you'd better get started on it."
"You mean you aren't going to do this for us?"
I said, "No, I'm not. I provided you with my work load figures, as you asked, but I'm not going to do your work for you."
Besides, I knew what would happen: I'd type it up, and it'd be bounced back to me six times for changes, and the other department would get all the credit for my work. So I was going to stop it before it got started.
Believe me, I knew what would happen because I had been through it. I typed up a list of approved abbreviations as a favor to my boss, and I was still getting that paper boomerang back three years later. Seriously. People would call me up and demand to know why I had put X abbreviation on there instead of Y abbreviation, and I'd tell them, "Hey, I'm just the typist. You need to talk to Colonel Painintheneck, who's the project officer." I did notice, however, that once I started referring people to him I got a lot fewer phone calls.
Your story always reminded me of an absurd statement (not so much a request or demand) that also belongs in the Professional Darwinism thread.
I worked for a commercial real estate brokerage and supported about five departments so the breakdown of which area paid what percentage was something like 40% sales/leasing, 40% property management, 20% finance. Well, I, one day, received a bunch of work from the staff at an apartment community we were managing stating that they were directed to give it to me to do. I was puzzled so I asked my office manager if I were now also supposed to be supporting the apartment communities with THEIR office work because I couldn't see the brokers being a) fine with me supporting those who don't work in our office (I supported our branch specifically) and b) fine with out-of-office work taking a higher priority than work in the office. She inquired with the property management director (who was already on thin ice because he was a newly-hired hothead who was so much alienating the staff in and out of the office that they were resigning). He said that if they were going to pay 40% of my salary, then he was going to use my time as he saw fit (I understood his reasoning but really didn't see that flying with the rest of the office). Well, she then asked me to determine exactly how much each area really used my time, I sent her the percentages and their amount they had to pay for got cut down to 12.5% (which was just enough time to do the stuff I'd regularly been doing for them each month). Yeah, not only did that crap not happen again (trying to give me out-of-office work), but the property management director also didn't last very long afterwards (seriously, I think he lasted just a few months).
Another place I used to work employed both me and my mother (I got her her job). She went on vacation one week, but everyone knew she was just taking time off and not actually going anywhere. During that time, our manager had a meeting that needed to take place, and he had the audacity to say to me, "Sorry, but this meeting is mandatory so you need to tell her that she has to interrupt her vacation to attend" (this was after I told him she was on vacation so she wouldn't be available to attend). I then looked at him and said, "Fine, but, next time, I'm telling her not to let anyone know she didn't go anywhere so you won't know she's in town so physically able to return to work when you say so." That got to him, and he immediately backpedaled and said she didn't have to attend the meeting.
Same company -- another person, knowing my mother and I lived together, tried to give me paperwork to give to her. I already hated this company and tried as much as I could to keep work and home life separate so my feeling was, outside of office hours, I did not let work permeate our lives. I refused the paperwork and told her that I wasn't responsible for providing another employee paperwork outside of my working hours just because we lived in the same place. That person then asked me how was my mother supposed to get the paperwork (my mother worked the graveyard shift at the time). I told that person it was her responsibility to get the paperwork to my mother, not mine. Yeah, she didn't like that answer, but, since I wasn't getting paid for delivering something outside of my work schedule (we were almost never authorized overtime), she couldn't force me to do it. After that, people knew never to try to force me to make THEIR jobs easier by passing on stuff (like work information) to her when I'd see her at home (we had other employees who were relatives or married, and I never did that to them either as I felt it wasn't fair to them -- that stupid job was stressful enough without making them take it into their personal lives).